The proliferation of high volume manufactured, portable electronic devices has encouraged innovation in both functional and aesthetic design practices for enclosures that encase such devices. Manufactured devices can include a housing that provides an ergonomic shape and aesthetically pleasing visual appearance desirable to the user of the device. Edge surfaces of housings, for example formed from metal compounds, can be shaped and finished to a desired geometry with a particular visual appearance. The edge surface can reveal minor variations in the final surface geometry or reflective appearance. Prior art techniques can result in a finish with an undesirable variation in geometry and in visually reflective appearance. Thus there exists a need for a method and an apparatus for polishing a curved edge of an object resulting in a geometrically uniform and consistent reflective appearance.